Control device of an inverted vehicle

ABSTRACT

The control device of the present invention applies only a damping to a vehicle if a load angular position is in the vicinity of a load angular position reference input. In the preferred embodiment, a control portion has a control switching unit and a switching linear torque unit. The switching linear torque unit calculates a damping torque and a linear feedback torque, the damping torque being obtained by applying a negative sign to a product of the load angular speed and the damping parameter, the linear feedback torque being obtained by multiplying at least one of a position tracking error, a speed tracking error, and an acceleration tracking error by a predetermined gain. The control switching unit switches and outputs the damping torque and the linear feedback torque. The control switching unit outputs the damping torque if the load angular position is in the vicinity of the load angular position reference input, and outputs the linear feedback torque otherwise. The embodiment enables the inverted vehicle to stably travel at a desired speed without vibration.

TECHNICAL FIELD

The present invention relates to a control device (control portion) ofan inverted vehicle, and particularly to the control device of theinverted vehicle which has wheel driving means and a link like load andmoves while balance controlling to maintain the link like load at aninverted state.

BACKGROUND ART

A vehicle which has a left and right pair of wheels coaxially disposedand moves while keeping at an inverted state is known. For example, aninverted two-wheels moving robot which autonomously moves while keepingthe inverted state is disclosed in patent document 1 (JapaneseUnexamined Patent Application Publication No. 2006-123014). A coaxialtwo-wheel vehicle which moves while balancing in a state in which ahuman stands on a step is disclosed in patent document 2 (JapaneseUnexamined Patent Application Publication No. 2006-315666).

FIG. 10 is a diagram showing a configuration of a controller of theinverted two-wheel moving robot disclosed in the patent document 1.

In FIG. 10, 1001 denotes a friction observer, 1002 denotes a targetstate generator, 1003 denotes state feedback gains, and 1004 denotes aninverted robot.

An angular speed reference input is input to the friction observer 1001,and the friction observer 1001 calculates a friction of a motor and afriction between a wheel and a road as an estimated friction and outputsthe estimated friction.

The angular speed reference input and the estimated friction are inputto the target state generator 1002, and the target state generator 1002calculates a target state of the inverted robot 1004 as a plant andoutputs the calculation result.

A signal in which a state variable of the inverted robot 1004 issubtracted from the target state is input to the state feedback gains1003, and the state feedback gains 1003 calculate state feedbacksignals, which make the inverted robot 1004 move in a desired manner,based on the input signal and output the state feedback signals.

The inverted robot 1004 is driven by the sum of the state feedbacksignals and the estimated friction.

As mentioned above, the conventional method of the inverted two-wheelmoving robot controls the motions of the inverted robot 1004 based on alinearized model which linearlizes the inverted robot 1004 as a plant inthe vicinity of a desired posture.

CITATION LIST Patent Literature

-   Patent document 1-   Japanese Unexamined Patent Application Publication No. 2006-123014    (FIG. 4)

SUMMARY OF INVENTION Technical Problem

As explained above, the conventional inverted control executes a simplelinear feedback control, however the inverted robot or the coaxialtwo-wheel vehicle has a structure in which a long link is disposed abovethe coaxial wheels, and which makes the link portion not stable at atarget posture and easy to swing.

There is a problem that the link portion is not stable at a targetposture and a vibration occurs in the vicinity of the target posture ifthe feedback control is continuously executed in accordance withtracking error from the target posture, for example, in the conventionalmethod.

Incidentally, feedback gains are adjusted to suppress the vibrations inthe vicinity of the target posture in the conventional method; howeverthe simple adjustment of the feedback gains is not sufficient tomaintain the vehicle at the target posture for the purpose of preventingoverturning when the posture is apart from the target posture and at thesame time to prevent vibrations in the vicinity of the target posture.

The present invention aims to provide the control device of the invertedvehicle which is capable of moving at a desired horizontal speed whileexecuting a stable inverted balance control without the vibrations.

Solution to Problem

The present invention has a following structure to solve the problemsmentioned above.

That is, the present invention provides a control device controlling atravel motion of an inverted vehicle which keeps an inverted state, theinverted vehicle having driving means having a wheel and a loadcontrolled to keep the inverted state above the wheel through a link,the control device executing the following control of: defining an anglebetween a straight line connecting a center of gravity of the load witha center of gravity of the wheel and a vertical straight line as a loadangular position; and applying only a damping to the inverted vehicle ifthe load angular position is in the vicinity of a load angular positionreference input as a desired load angular position.

In the present invention, it is preferable that a damping range as awidth in the vicinity of the load angular position reference input iscalculated by multiplying an absolute value of the load angular positionreference input by a predetermined coefficient.

In the present invention, it is preferable to define the damping as aviscous friction.

In the present invention, it is preferable that a damping parameter asthe viscous friction is calculated as a function of a load angularposition tracking error and the load angular position reference input,the load angular position tracking error being defined as a value inwhich the load angular position is subtracted from the load angularposition reference input.

In the present invention, it is preferable that the damping parameter iscalculated by subtracting half of the absolute value of the load angularposition reference input from the load angular position tracking error,dividing an absolute value of the subtracted value by the absolute valueof the load angular position reference input, and multiplying thedivided value by a constant.

In the present invention, it is preferable that the damping parameter asthe viscous friction is defined as a constant value.

In the present invention, it is preferable that the control device has:a switching linear torque unit calculating a damping torque and a linearfeedback torque, the damping torque being obtained by applying anegative sign to a product of the load angular speed and the dampingparameter, the linear feedback torque being obtained by multiplying atleast one of a position tracking error, a speed tracking error, and anacceleration tracking error by a predetermined gain; and a controlswitching unit switching and outputting the damping torque and thelinear feedback torque calculated by the switching linear torque unit.

In the present invention, it is preferable that the control switchingunit outputs the damping torque if 0≦sgn (θ₁*)•e<h, and outputs thelinear feedback torque otherwise where e=θ₁*−θ₁ is satisfied, θ₁* is theload angular position reference input, θ₁ is the load angular position,sgn (•) is a signum function indicating +1 if • is positive, −1 if • isnegative, and 0 if • is zero, and h is the damping range calculated bymultiplying the absolute value of the load angular position referenceinput by a predetermined coefficient.

ADVANTAGEOUS EFFECTS OF INVENTION

According to the present invention as mentioned above, it is possible toprevent the load angular position of the vehicle from vibrating in thevicinity of a desired value. Then, it is possible to converge the loadangular position of the vehicle on the desired value without thevibration, and the vehicle can safely move at a desired speed.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows a first embodiment according to an inverted vehicle of thepresent invention.

FIG. 2 shows a model of the vehicle.

FIG. 3 shows a simulation result of the load angular position.

FIG. 4 shows a simulation result of wheel horizontal speed.

FIG. 5 shows the first modified example.

FIG. 6 shows the second modified example.

FIG. 7 shows a coaxial two-wheel vehicle as the inverted vehicle.

FIG. 8 shows an inverted autonomous moving robot as the invertedvehicle.

FIG. 9 shows an inverted vehicle having a link mechanism swingablydisposed above wheel driving means for four wheels.

FIG. 10 shows a diagram of a controller of an inverted two-wheel movingrobot in the conventional method.

DESCRIPTION OF EMBODIMENTS First Embodiment

An embodiment according to the present invention is explainedhereinafter with referring to drawings.

FIG. 1 shows the first embodiment according to an inverted vehicle ofthe present invention.

The inverted vehicle has a vehicle 141 as a plant, sensors 142 measuringthe states of the vehicle 141, a reference portion 100 generating adesired target state, and a control portion 110 executing control basedon measurement signals from the sensors 142 and a reference input fromthe reference portion 100.

The vehicle 141 is generally exemplified by a coaxial two-wheel vehicle(FIG. 7), an inverted type autonomous moving robot (FIG. 8), and so on.

The vehicle is not limited to above examples and might be a vehiclewhich has driving means with wheel and a link like load, and executes abalance control to maintain the link-like load at an inverted state.

For example, the vehicle might be a structure illustrated in FIG. 9.

FIG. 9 is a structure in which a link mechanism 902 is swingablydisposed above wheel driving means 901 for four wheels.

For example, an upper side of the link mechanism 902 might be formedlike a basket 903, so that the wheel driving means 401 may carry goodsin the basket 903.

Hereinafter, the vehicle 141 as mentioned above is modeled on FIG. 2 orthe like.

In FIG. 2, 201 denotes a load, 202 denotes wheels, and 203 denotes aroad.

The vehicle 141 keeps an inverted state and moves as illustrated in FIG.2.

The load 201 is a body of a robot, a passenger or a baggage mounted onthe vehicle 141.

The wheels 202 carry the load 201 and propel the load 201 using afriction force acting on the road 203.

The sensors 142 measure an angle (θ₁) of the load 201 and an angle (θ₂)of the wheel 202.

The reference portion 100 has a wheel horizontal speed reference inputgenerator 101 and a load angular position reference input unit 102.

The wheel horizontal speed reference input generator 101 generates andoutputs a wheel horizontal speed reference input as a desired horizontalmoving speed of the wheel 202 of the vehicle 141.

The load angular position reference input unit 102 to which the wheelhorizontal speed reference is input calculates and outputs a loadangular position reference input such that the wheel horizontal speedtracks the wheel horizontal speed reference input when the road 203 onwhich the vehicle 141 moves is horizontal.

The control portion 110 has a switching linear control portion 120, anonlinear control portion 130, and a torque reference input unit 111.

The switching linear control unit 120 has a damping range unit 121, adamping parameter unit 122, a switching linear torque unit 123, and acontrol switching unit 124.

The load angular position reference input from the load angular positionreference input unit 102, the load angular position θ₁, and the wheelangle θ₂, both being measurement signals from sensors 142, are input tothe damping range unit 121.

The damping range unit 121 calculates a range of the load angularposition as a damping range within which only a viscous friction isadded by the control of the vehicle 141, as based on the input signalsand outputs the calculation result.

The load angular position reference input (θ₁*) from the load angularposition reference input unit 102, the load angular position (θ₁), andthe wheel angle (θ₂), both being measurement signals from sensors 142,are input to the damping parameter unit 122.

The damping parameter unit 122 calculates based on the input signals andoutputs a damping parameter, which is used for a control within thedamping range.

The load angular position reference input (θ₁*) from the load angularposition reference input unit 102, the damping parameter from thedamping parameter unit 122, the load angular position (θ₁), and thewheel angle (θ₂), both being measurement signals from sensors 142, areinput to the switching linear torque unit 123.

The switching linear torque unit 123 calculates and outputs a dampingtorque and a linear feedback torque. The damping torque is obtained bychanging the sign of a product of the load angular speed and the dampingparameter, and the linear feedback torque is obtained by multiplying atleast one of a position tracking error, a speed tracking error, and anacceleration tracking error, and a predetermined gain.

The damping range calculated by the damping range unit 121, themeasurement signals from sensors 142, and the switching linear torquecalculated by the switching linear torque unit 123 are input to thecontrol switching unit 124. The control switching unit 124 outputs theswitching linear torque calculated by the switching linear torque unit123 while switching.

The nonlinear control unit 130 has a wheel vertical accelerationobserver 131, a wheel horizontal speed observer 132, and a nonlineartorque unit 133.

The measurement signals from the sensors 142 are input to the wheelvertical acceleration observer 131, and the wheel vertical accelerationobserver 131 estimates a vertical acceleration of the wheel 202 based onthe input signals and outputs the estimation result as an estimatedwheel vertical speed.

The measurement signals are input to the wheel horizontal speed observer132, and the wheel horizontal speed observer 132 estimates a horizontalspeed of wheel 202 based on the input signals and outputs it as anestimated wheel horizontal speed.

The estimated wheel vertical acceleration and the estimated wheelhorizontal speed are input to the nonlinear torque unit 133, and thenonlinear torque unit 133 calculates and outputs a nonlinear torqueindicating nonlinear dynamics of the vehicle 141.

The switching linear torque, which is switched and output by the controlswitching unit 124, and the nonlinear torque, which is output fromnonlinear torque unit 133, are input to the torque reference input unit111, and the torque reference input unit 111 outputs a torque referenceinput obtained by dividing a sum of these input signals and a radius ofthe wheel 202.

The vehicle 141 is driven by the torque reference input.

Hereinafter, a detailed control mechanism of the control portion 110according to the first embodiment for motion cotrol of the vehicle 141is explained.

In FIG. 2, the parameters are set as described below.

The symbol m₁ is a load mass,

J₁ is a load inertia moment,

m₂ is a wheel mass,

J₂ is a wheel inertia moment,

I is a distance between the center of gravity of the load and the centerof the gravity of the wheel,

r is a wheel radius,

θ₁ is the load angular position,

θ₂ is the wheel angle, and

T_(ref) is the torque reference input.

Furthermore, assuming that a wheel horizontal position is x₂ and a wheelvertical position is y₂, and a load horizontal position x₁ and a loadvertical position y₁ are respectively described by a equation (1) and aequation (2) as indicated below.

Equation 1

x ₁ =l sin θ₁ +x ₂  (1)

Equation 2

y ₁ =l cos θ₁ +y ₂  (2)

A kinetic energy T and a potential energy V of the vehicle 141 arerespectively described by a equation (3) and a equation (4) as indicatedbelow using equation (1) and equation (2).

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack & \; \\\begin{matrix}{T = {{\frac{1}{2}{m_{1}\left( {{\overset{.}{x}}_{1}^{2} + {\overset{.}{y}}_{1}^{2}} \right)}} + {\frac{1}{2}J_{1}{\overset{.}{\theta}}_{1}^{2}} +}} \\{{{\frac{1}{2}{m_{2}\left( {{\overset{.}{x}}_{2}^{2} + {\overset{.}{y}}_{2}^{2}} \right)}} + {\frac{1}{2}J_{2}{\overset{.}{\theta}}_{2}^{2}}}} \\{= {{\frac{1}{2}{m_{1}\begin{pmatrix}{{\overset{.}{x}}_{2}^{2} + {\overset{.}{y}}_{2}^{2} + {l^{2}{\overset{.}{\theta}}_{1}^{2}} +} \\{{2l\; {\overset{.}{\theta}}_{1}{\overset{.}{x}}_{2}\cos \; \theta_{1}} +} \\{{2r\; {\overset{.}{\theta}}_{2}{\overset{.}{x}}_{2}} - {2l\; {\overset{.}{\theta}}_{1}{\overset{.}{y}}_{2}\sin \; \theta_{1}}}\end{pmatrix}}} +}} \\{{{\frac{1}{2}J_{1}{\overset{.}{\theta}}_{1}^{2}} + {\frac{1}{2}{m_{2}\left( {{\overset{.}{x}}_{2}^{2} + {\overset{.}{y}}_{2}^{2}} \right)}} + {\frac{1}{2}J_{2}{\overset{.}{\theta}}_{2}^{2}}}}\end{matrix} & (3)\end{matrix}$Equation 4

V=m ₁ gy ₁ +m ₂ gy ₂  (4)

Then, the equation of motion of the vehicle 141 is derived as equations(5) through (8) using the Euler-Lagrange equation.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack & \; \\{{{\left( {{m_{1}l^{2}} + J_{1}} \right){\overset{¨}{\theta}}_{1}} + {m_{1}l\; {\overset{¨}{x}}_{2}\cos \; \theta_{1}} - {m_{1}l\; {\overset{¨}{y}}_{2}\sin \; \theta_{1}} - {m_{1}l\; {\overset{.}{\theta}}_{1}{\overset{.}{x}}_{2}\sin \; \theta_{1}} - {m_{1}l\; {\overset{.}{\theta}}_{1}{\overset{.}{y}}_{2}\cos \; \theta_{1}} + {m_{1}l\; {\overset{.}{\theta}}_{1}{\overset{¨}{x}}_{2}\sin \; \theta_{1}} + {m_{1}l\; {\overset{¨}{\theta}}_{1}{\overset{.}{x}}_{2}\; \sin \; \theta_{1}} + {m_{1}l\; {\overset{.}{\theta}}_{1}^{2}{\overset{.}{x}}_{2}\cos \; \theta_{1}} + {m_{1}l\; {\overset{¨}{\theta}}_{1}{\overset{.}{y}}_{2}\cos \; \theta_{1}} + {m_{1}l\; {\overset{.}{\theta}}_{1}{\overset{¨}{y}}_{2}\cos \; \theta_{1}} - {m_{1}l\; {\overset{.}{\theta}}_{1}^{2}{\overset{.}{y}}_{2}\sin \; \theta_{1}}} = 0} & (5)\end{matrix}$Equation 6

J₂{umlaut over (θ)}₂=T_(ref)  (6)

Equation 7

(m ₁ +m ₂){umlaut over (x)} ₂ +m ₁ l{umlaut over (x)} ₂ cos θ₁ −m ₁l{dot over (θ)} ₁ {dot over (x)} ₂ sin θ₁=0  (7)

Equation 8

(m ₁ +m ₂)ÿ ₂ −m ₁ l{umlaut over (θ)} ₁ sin θ₁ −m ₁ l{dot over (θ)} ₁ ²cos θ₁ +m ₂ g=0  (8)

The symbol g is the gravitational acceleration.

Furthermore, equation (6) and equation (7) are rewritten as equation (9)and equation (10) taking into account a viscous friction between thewheel 202 and the road 203.

The symbol D is the viscous friction coefficient.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack & \; \\{{{J_{2}{\overset{¨}{\theta}}_{2}} + {D\left( {{\overset{.}{\theta}}_{2} - \frac{{\overset{.}{x}}_{2}}{r}} \right)}} = T_{ref}} & (9)\end{matrix}$Equation 10

(m ₁ +m ₂){umlaut over (x)} ₂ +m ₁ l{umlaut over (x)} ₂ cos θ₁ −m ₁l{dot over (θ)} ₁ {dot over (x)} ₂ sin θ₁ D(r{dot over (θ)} ₂ −{dot over(x)} ₂)=0  (10)

Equation (11) is derived from equation (9) and equation (10).

Equation 1

(m ₁ +m ₂){umlaut over (x)} ₂ +m ₁ l{umlaut over (x)} ₂ cos θ₁ −m ₁l{dot over (θ)} ₁ {dot over (x)} ₂ sin θ₁ −rJ ₂{umlaut over (θ)}₂ =−rT_(ref)  (11)

Equation (12) is obtained by subtracting equation (11) from equation(5).

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack & \; \\{{{{{\left( {{m_{1}l^{2}} + J_{1}} \right){\overset{¨}{\theta}}_{1}} + N_{x} + N_{y}} = {r\; T_{ref}}}\mspace{14mu} {N_{x} = {{{{- \left( {m_{1} + m_{2}} \right)}{\overset{¨}{x}}_{2}} + {m_{1}l\; {\overset{.}{\theta}}_{1}{\overset{¨}{x}}_{2}\sin \; \theta_{1}} + {m_{1}l\; {\overset{¨}{\theta}}_{1}{\overset{.}{x}}_{2}\sin \; \theta_{1}} + {m_{1}l\; {\overset{.}{\theta}}_{1}^{2}{\overset{.}{x}}_{2}\cos \; \theta_{1}N_{y}}} = {{r\; J_{2}{\overset{¨}{\theta}}_{2}} - {m_{1}l\; {\overset{¨}{y}}_{2}\sin \; \theta_{1}} - {m_{1}l\; {\overset{.}{\theta}}_{1}{\overset{.}{y}}_{2}\cos \; \theta_{1}} + {m_{1}l\; {\overset{¨}{\theta}}_{1}{\overset{.}{y}}_{2}\cos \; \theta_{1}} + {m_{1}l\; {\overset{.}{\theta}}_{1}{\overset{¨}{y}}_{2}\cos \; \theta_{1}} - {m_{1}l\; {\overset{.}{\theta}}_{1}^{2}{\overset{.}{y}}_{2}\sin \; \theta_{1}}}}}}\mspace{11mu}} & (12)\end{matrix}$

The symbol N_(X) is a nonlinear term that is a function of the wheelhorizontal position x₂, and the symbol N_(y) is a nonlinear term that isa function of the wheel vertical position y₂.

Assuming that the load angular position θ₁ varies much slower than thewheel horizontal position x₂, equation (11) is rewritten as equation(13).

Equation 13

c ₁ {umlaut over (x)} ₂ +c ₂ {dot over (x)} ₂ =rJ ₂{umlaut over (θ)}₂−rT _(ref)

c ₁ =m ₁ +m ₂ +m ₁ l cos θ₁

c ₂ =−m ₁ l{dot over (θ)} ₁ sin θ₁  (13)

Portions of equation (13) varying much slower than the wheel horizontalposition x₂ are expressed as constants c1, c2 and c3.

A wheel horizontal speed dx₂/dt is described as equation (14) usingequation (13).

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack & \; \\{{\overset{.}{x}}_{2} = {L^{- 1}\left\{ {\frac{1}{{c_{1}s} + c_{2}}\left( {{s^{2}\Theta_{2}} - {r\; T_{ref}}} \right)} \right\}}} & (14)\end{matrix}$

The symbol s²·Θ₂ is the Laplace transform of a wheel acceleration(d²θ₂/dt²), and the symbol L is the Laplace transform.

The wheel horizontal speed observer 132 calculates the estimated wheelhorizontal speed using equation (14).

Meanwhile, equation (15) is derived by solving equation (8) for a wheelvertical acceleration (d²y₂/dt²).

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack & \; \\{{\overset{¨}{y}}_{2} = \frac{{m_{1}l\; {\overset{¨}{\theta}}_{1}\sin \; \theta_{1}} + {m_{1}l\; {\overset{.}{\theta}}_{1}^{2}\cos \; \theta_{1}} - {m_{2}g}}{\left( {m_{1} + m_{2}} \right)}} & (15)\end{matrix}$

The wheel vertical acceleration observer 131 calculates the estimatedwheel vertical acceleration using equation (15).

Assuming that the wheel horizontal speed reference input is v₂* (=thefirst order time derivative of x₂*), the load angular position referenceinput θ₁*, which is the load angular position θ₁ when the wheelhorizontal speed (dx₂/dt) equals to the wheel horizontal speed referenceinput v₂* for the flat road 203, is described by equation (16). That is,the load angular position reference input θ₁* is the arctangent of thevalue obtained by dividing the wheel horizontal speed reference input bythe gravitational acceleration.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack & \; \\{\theta_{1}^{*} = {\tan^{- 1}\frac{{\overset{¨}{x}}_{2}^{*}}{g}}} & (16)\end{matrix}$

The wheel horizontal speed reference input generator 101 outputs thewheel horizontal speed reference input v₂* (=the first order timederivative of x₂*), and the load angular position reference input unit102 calculates the load angular position reference input θ₁* usingequation (16) and outputs the calculation result.

Equation (17) is derived by substituting equation (14) and equation (15)into equation (12).

Equation 17

(m ₁ l ² +J ₁){umlaut over (θ)}₁ +N ^(x) +N _(y) =rT _(ref)  (17)

Equation (17) is rewritten as equation (18).

Equation 18

(m ₁ l ² +J ₁){umlaut over (θ)}₁ =u

u=rT _(ref) −N _(x) −N _(y)  (18)

The symbol u is the switching linear torque.

Then, consider the switching linear torque u in equation (19) such thatthe load angular position θ₁ converges to the load angular positionreference input θ₁*.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack & \; \\{u = \left\{ \begin{matrix}{{\beta \; \overset{.}{e}} + {\kappa }} & {{{{sgn}\left( \theta_{1}^{*} \right)}} < 0} \\{{- \gamma}\; {\overset{.}{\theta}}_{1}} & {0 \leq {{{sgn}\left( \theta_{1}^{*} \right)}\; } < h} \\{{\beta \; \overset{.}{e}} + {\kappa \; }} & {{{{sgn}\left( \theta_{1}^{*} \right)}} \geq h}\end{matrix} \right.} & (19)\end{matrix}$

Where, e=θ₁*−θ₁ is the load angular position tracking error,

β is a speed proportional control gain,

θ is a position proportional control gain,

γ is the damping parameter, and

sgn (•) is the signum function indicating +1 if • is positive, −1 if •is negative, and 0 if • is zero.

Further, h=c|θ₁*| is the damping range to prevent a chattering by thefeedback control, and c is a parameter of the damping range h.

The switching torque u in equation (19) implies that it is possible tostably converge the load angular position θ₁ on the load angularposition reference input θ₁* without chattering by causing a motion ofthe load 201 having viscous friction with the damping parameter γ whenthe tracking error between the load angular position θ₁ and the loadangular position reference input θ₁* is small, in particular, when thetracking error in the direction of decrease of the absolute value of theload angular position θ₁ is within the damping range h.

Furthermore, the switching torque u implies that it is possible toconverge the load angular position θ₁ on the load angular positionreference input θ₁* doing a feedback control with stiffness given by theposition proportional control gain κ and with the viscous friction givenby the speed proportional control gain β when the tracking error isoutside of the damping range h.

It is preferable to set the damping parameter γ as a function of theload angular position reference input θ₁* and the load angular positiontracking error e as in equation (20), for example.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack & \; \\{\gamma = {\frac{2\; \beta}{\theta_{1}^{*}}{{ - \frac{\theta_{1}^{*}}{2}}}}} & (20)\end{matrix}$

In other words, the switching linear control unit 120 receives the loadangular position reference input θ₁* from the load angular positionreference input unit 102, and the load angular position reference inputθ₁* is input to the damping range unit 121, damping parameter unit 122,and switching linear torque unit 123.

Then, the damping range unit 121 calculates the damping range ash=c|θ₁*| using the load angular position reference input θ₁* andparameter c.

The obtained damping range h is output to the control switching unit124.

The damping parameter unit 122 calculates the damping parameter γ inaccordance with equation (20), and outputs the calculation result to theswitching linear torque unit 123.

The switching linear torque unit 123 calculates the switching lineartorque u described in equation (19) using the damping parameter γ fromthe damping parameter unit 122, the speed proportional control gain β,and the position proportional control gain κ, both gains beingpreviously determined.

The calculated switching linear torque u is output to the controlswitching unit 124.

The control switching unit 124 switches and selects the switching lineartorque u calculated by the switching linear torque unit 123 withreference to the load angular position tracking error e and the dampingrange h.

The switching linear torque selected by the control switching unit 124is output to the torque reference input unit 111.

Furthermore, the nonlinear torque unit 133 calculates the nonlineartorque as Nx+Ny in equation (12) based on the estimated wheel verticalacceleration calculated using equation (15) and the estimated wheelhorizontal speed calculated using equation (14) and outputs thecalculation result.

The torque reference input unit 111 calculates the torque referenceinput T_(ref) using the switching linear torque u and the nonlineartorque Nx+Ny in accordance with equation (21) and output the calculationresult.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack & \; \\{T_{ref} = \frac{u + N_{x} + N_{y}}{r}} & (21)\end{matrix}$

Where, r is the wheel radius.

The vehicle 141 is driven and controlled by the torque T_(ref).

The first embodiment having the structure as described above hasfollowing effects.

(1) In the first embodiment, the load angular position θ₁ is dividedinto three ranges as described in equation (19), and the optimum torquereference input can be calculated in each range.

Furthermore, the control switching unit 124 switches the controldepending on whether within the damping range or out of the dampingrange.

Therefore, it is possible to smoothly converge the load angular positionθ₁ on the load angular position reference input θ₁* without thevibration of the load angular position θ₁ in the vicinity of the loadangular position reference input θ₁*.

As a result, it is possible to accomplish a stable horizontal travelmotion.

(2) The damping parameter unit 122 is disposed and the damping parameterγ is set by equation (20). Therefore, it is possible to converge theload angular position θ₁ on the load angular position reference inputθ₁* more smoothly and quickly than when the damping parameter γ is aconstant value.

(3) The vehicle 141 is controlled using the estimated wheel horizontalspeed in equation (14), and it is possible to converge the wheelhorizontal speed v₂ (=the first order time derivative of x₂) of thevehicle 141 on the wheel horizontal speed reference input v₂* (=thefirst order time derivative of x₂*) if the wheel 202 relatively slips onthe road 203.

(4) The vehicle 141 is controlled using the estimated wheel verticalacceleration in equation (15), and it is possible to stably control theload angular position θ₁ as long as the wheel 202 contacts with the road203, even if the road 203 is bumpy.

An Experimental Example

Hereinafter, an experimental example verifying the effects of thepresent invention is described.

A simulation result of the first embodiment is described as theexperimental example.

Here are the values used for the simulation:

m₁=70 [kg],

J₁=25.2 [kg·m²],

m₂=15 [kg],

J₂=0.075 [kg·m²],

l=0.9 [m],

r=0.1 [m],

D=0.1 [N·s/m],

g=9.8 [m/s²],

T=1×10⁻³ [s],

κ=40 [s⁻¹]

J₁₀=m₁×I²+J₁ [kg·m²],

β₀=2πκ [s⁻¹],

β=β₀×J₁₀ [N·m·s/rad],

γ=0.1 [N·m·s/rad],

pc1=[−49.9,−201.4] [rad/s], and

td=0.5 [s].

Where, m1 is the load mass,

J₁ is the load inertia moment,

m₂ is the wheel mass,

J₂ is the wheel inertia moment,

l is the distance between the center of gravity of the load and thecenter of gravity of the wheel,

r is the wheel radius,

D is the viscous friction between the wheel and the road,

g is the gravitational acceleration,

T is a sampling time,

κ is the position proportional control gain according to the presentinvention,

J₁₀ is a nominal inertia moment,

β₀ is a normalized speed proportional control gain according to thepresent invention,

β is a speed proportional control gain according to the presentinvention,

γ is the friction parameter according to the present invention,

pc1 is a closed loop pole according to the conventional method, and

td is an impulse disturbance time.

The viscous friction between the wheel and the road D is a viscousfriction acting between the wheel 202 and the road 203 illustrated inFIG. 2.

The nominal inertia moment J₁₀ is a parameter normalizing a speedcontrol loop in the present invention.

The symbol pc1 is a pole of a closed loop disposed at a state feedbackcontrol according to the conventional method.

Consider a case that there is an impulse-like acceleration disturbanceinput to the wheel 202 in the upward vertical direction at the impulsedisturbance time td.

FIG. 3 and FIG. 4 are plots showing the simulation result.

FIG. 3 shows a variation of the load angular position.

In FIG. 3, a solid line L₁₀ denotes the load angular position withproposed control, the broken line L₁₁ denotes the load angular positionreference input, and the chain line L₁₂ denotes the load angularposition with the conventional method.

It turns out that the present invention and the conventional methodequally track the load angular position reference input before the 0.5[s] when the acceleration disturbance is applied; however, after 0.5[s],the load angular position oscillates in the conventional method, on theother hand, the load angular position continues to track the loadangular position reference input without the oscillation after theacceleration disturbance is applied in the present invention.

Then, the time change of the load angular position of the presentinvention becomes a polygonal line due to the control applying only thedamping within the damping range in equation (19). This implies that itis difficult for the load angular position to vibrate in the vicinity ofthe load angular position reference input by employing the dampingrange.

Furthermore, the wheel vertical acceleration observer 131 calculates theestimated wheel vertical acceleration in equation the (15), and thenonlinear torque unit 133 calculates the nonlinear torque Ny. As aresult, it is possible to compensate the acceleration disturbanceapplied to the wheel 202 in the vertical direction due to the bumps onthe road 203. This shows that it is possible to stabilize the loadangular position in the present invention even if the accelerationdisturbance is applied.

FIG. 4 shows a variation of the horizontal speed of the wheel.

In FIG. 4, a solid line L₂₀ denotes the wheel horizontal speed with theproposed control, the broken line L₂₁ denotes the desired wheelhorizontal speed, and the chain line L₂₂ denotes the wheel horizontalspeed with the conventional method.

It turns out that both the present invention and the conventional methodtrack the desired wheel horizontal speed before 0.5 [s] when theacceleration disturbance is applied; however, after 0.5[s], the wheelhorizontal speed becomes vibrational in the conventional method, on theother hand, the wheel horizontal speed does not become vibrational andtracks the desired wheel horizontal speed in the present invention.

Modified Example 1

In the first embodiment, the damping parameter γ is calculated by thedamping parameter unit 122 in accordance with equation (20); however,the damping parameter γ may be a predetermined fixed value.

In other words, the predetermined damping parameter may be set andstored to a damping parameter memory (damping parameter memory) 125 asshown in FIG. 5. Then, the damping parameter memory 125 may supply avalue of the damping parameter γ to the switching linear torque unit123.

Modified Example 2

In the first embodiment, it is explained as the most preferableembodiment that the nonlinear control unit 130 is disposed. However, itis not be necessary to dispose the nonlinear control unit 130 if astable control which smoothly converges the load angular position θ₁ onthe load angular position reference input θ₁* is accomplished withoutthe vibration in the vicinity of the load angular position referenceinput θ₁*.

In other words, the nonlinear control unit 130 may be omitted from thecontrol portion 610 as illustrated in FIG. 6.

Here, if the nonlinear control unit 130 is omitted and only theswitching linear control unit 120 is disposed, it is preferable to setthe gains to suppress the nonlinear terms as the disturbance as much aspossible, by adjusting the gains of the linear feedback torque of theswitching linear torque u calculated in the switching linear torque unit123.

Needless to say, it is preferable to dispose the nonlinear control unit130 to take into account the nonlinear terms due to travelling on theuneven and bumpy road, a collision with an obstacle, and a slipping ofthe wheel.

The present invention is not limited to the above embodiments andincludes modifications and improvements within a range accomplishing thepurpose of the present invention.

For example, the position P/speed P control may be replaced with anycontrol law such as the position P/speed PI control, the positionP/speed I-P control, and the position PID control in equation (19).

This application is based on and claims the benefit of priority fromJapanese patent application No. 2009-109591, filed on Apr. 28, 2009, thedisclosure of which is incorporated herein its entirety by reference.

INDUSTRIAL APPLICABILITY

According to the present invention, the inverted two-wheel vehicle canmove at the desired horizontal speed without a turnover and anoscillation even if there is unevenness on the road or even if thevehicle collides with a human or an object. Therefore, the presentinvention is widely applicable to a two-wheel robot travelling at theinverted state, an electric wheelchair, an automatic delivery device, arobot working at narrow space such as a lifesaving at the time ofdisaster, an assembly apparatus assembling the electric device sensitiveto a vibration, and so on.

REFERENCE SIGNS LIST

-   -   100 REFERENCE PORTION    -   101 WHEEL HORIZONTAL SPEED REFERENCE INPUT GENERATOR    -   102 LOAD ANGULAR POSITION REFERENCE INPUT UNIT    -   110, 610 CONTROL PORTION    -   111 TORQUE REFERENCE INPUT UNIT    -   120 SWITCHING LINEAR CONTROL UNIT    -   121 DAMPING RANGE UNIT    -   122 DAMPING PARAMETER UNIT    -   123 SWITCHING LINEAR TORQUE UNIT    -   124 CONTROL SWITCHING UNIT    -   125 DAMPING PARAMETER MEMORY    -   130 NONLINEAR CONTROL UNIT    -   131 WHEEL VERTICAL ACCELERATION OBSERVER    -   132 WHEEL HORIZONTAL SPEED OBSERVER    -   133 NONLINEAR TORQUE UNIT    -   141 VEHICLE    -   142 SENSORS    -   201 LOAD    -   202 WHEEL    -   203 ROAD    -   1001 FRICTION OBSERVER    -   1002 TARGET STATE GENERATOR    -   1003 STATE FEEDBACK GAINS    -   1004 INVERTED ROBOT

1. A control device controlling motions of an inverted vehicle whichkeeps an inverted state, the inverted vehicle having driving meanshaving a wheel and a load controlled to keep the inverted state abovethe wheel through a link, the control device executing the followingcontrol of: defining an angle between a straight line connecting acenter of gravity of the load with a center of gravity of the wheel anda vertical straight line as a load angular position; and applying only adamping to the inverted vehicle if the load angular position is in thevicinity of a load angular position reference input that is a desiredload angular position.
 2. The control device of the inverted vehicleaccording to claim 1, wherein a damping range as a width in the vicinityof the load angular position reference input is calculated bymultiplying an absolute value of the load angular position referenceinput by a predetermined coefficient.
 3. The control device of theinverted vehicle according to claim 1 or 2, wherein the damping isdefined as a viscous friction.
 4. The control device of the invertedvehicle according to claim 3, wherein a damping parameter as the viscousfriction is calculated as a function of a load angular position trackingerror and the load angular position reference input, where the loadangular position tracking error is obtained by subtracting the loadangular position from the load angular position reference input.
 5. Thecontrol device of the inverted vehicle according to claim 4, wherein thedamping parameter is calculated by subtracting half of an absolute valueof the load angular position reference input from the load angularposition tracking error, dividing an absolute value of the subtractedvalue by the absolute value of the load angular position referenceinput, and multiplying the divided value by a constant.
 6. The controldevice of the inverted vehicle according to claim 3, wherein the dampingparameter as the viscous friction is defined as a constant value.
 7. Thecontrol device of the inverted vehicle according to any one of claim 4to claim 6, the control device comprising: a switching linear torqueunit calculating a damping torque and a linear feedback torque, thedamping torque being obtained by applying a negative sign to a productof the load angular speed and the damping parameter, the linear feedbacktorque being obtained by multiplying at least one of a position trackingerror, a speed tracking error, and an acceleration tracking error by apredetermined gain; and a control switching unit switching andoutputting the damping torque and the linear feedback torque calculatedby the switching linear torque unit.
 8. The control device of theinverted vehicle according to claim 7, wherein the control switchingunit outputs the damping torque if 0≦sgn (θ₁*)•e<h, and outputs thelinear feedback torque otherwise, where e=θ₁*−θ₁ holds, θ₁* is the loadangular position reference input, θ₁ is the load angular position, sgn(•) is a signum function indicating +1 if • is positive, −1 if • isnegative, and 0 if • is zero, and h is the damping range calculated bymultiplying the absolute value of the load angular position referenceinput by a predetermined coefficient.